We consider an inverse problem for a system of isotropic elasticity equations in a sphere domain. The linearized problem of identification of three characteristics of elastic isotropic medium is investigated. It is supposed that the medium density ρ(r) depends on the radial variable only and the propagation velocity of longitudinal c(r, θ ϕ) and transverse a(r, θ, ϕ) waves can be represented as a ²(r; θ, ϕ) = a ² ₀ + a ₁(r, θ, ϕ), c ²(r, θ, ϕ) = c ² ₀ + c ₁(r, θ, ϕ), where a ² ₀, c ² ₀ are some known constants, and unknown functions a ₁(r, θ, ϕ), c ₁(r, θ, ϕ) are small in comparison with the constants a ² ₀ and c ² ₀ correspondingly. The uniqueness theorem is proved and estimates of conditional stability of the inverse problem solution are obtained.